Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 170 | 168 | 272 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.00 | 0.99 | 1.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.636 | 0.010 | 1.553 | 0.000 | 0.000 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 260 | 256 | 240 | 0 | 0 | 0 | 0 | 0 | 16 | 0 |
N.S. |
1 | 0.98 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.992 | 0.097 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 348 | 346 | 322 | 0 | 0 | 0 | 0 | 0 | 16 | 0 |
N.S. |
1 | 0.99 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.663 | 0.039 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 202 | 166 | 242 | 230 | 214 | 316 | 0 | 285 | 0 |
N.S. |
1 | 1.10 | 0.90 | 1.32 | 1.25 | 1.16 | 1.72 | 0.00 | 1.55 | 0.00 |
time (sec) |
N/A | 0.662 | 0.110 | 0.428 | 0.037 | 0.105 | 0.344 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 147 | 121 | 174 | 150 | 147 | 190 | 0 | 181 | 0 |
N.S. |
1 | 1.11 | 0.91 | 1.31 | 1.13 | 1.11 | 1.43 | 0.00 | 1.36 | 0.00 |
time (sec) |
N/A | 0.518 | 0.073 | 0.441 | 0.038 | 0.091 | 0.254 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 106 | 91 | 84 | 82 | 87 | 99 | 122 | 108 | 78 |
N.S. |
1 | 1.15 | 0.99 | 0.91 | 0.89 | 0.95 | 1.08 | 1.33 | 1.17 | 0.85 |
time (sec) |
N/A | 0.340 | 0.027 | 0.345 | 0.029 | 0.104 | 0.181 | 0.180 | 0.172 | 2.911 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 30 | 29 | 30 | 43 | 26 | 41 | 30 | 28 |
N.S. |
1 | 1.00 | 1.00 | 0.97 | 1.00 | 1.43 | 0.87 | 1.37 | 1.00 | 0.93 |
time (sec) |
N/A | 0.196 | 0.006 | 0.312 | 0.035 | 0.091 | 0.072 | 0.109 | 0.169 | 2.786 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 187 | 175 | 279 | 0 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 0.94 | 1.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.670 | 0.047 | 1.663 | 0.000 | 0.000 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 79 | 174 | 103 | 253 | 0 | 234 | 75 | 0 |
N.S. |
1 | 1.00 | 0.96 | 2.12 | 1.26 | 3.09 | 0.00 | 2.85 | 0.91 | 0.00 |
time (sec) |
N/A | 0.252 | 0.073 | 4.262 | 0.040 | 0.115 | 0.000 | 0.374 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 129 | 166 | 273 | 158 | 566 | 0 | 0 | 159 | 0 |
N.S. |
1 | 1.01 | 1.30 | 2.13 | 1.23 | 4.42 | 0.00 | 0.00 | 1.24 | 0.00 |
time (sec) |
N/A | 0.317 | 0.239 | 5.029 | 0.045 | 0.169 | 0.000 | 0.000 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 199 | 205 | 510 | 0 | 977 | 0 | 0 | 262 | 0 |
N.S. |
1 | 1.09 | 1.12 | 2.79 | 0.00 | 5.34 | 0.00 | 0.00 | 1.43 | 0.00 |
time (sec) |
N/A | 0.367 | 0.280 | 4.764 | 0.000 | 0.490 | 0.000 | 0.000 | 5.556 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 368 | 387 | 354 | 526 | 590 | 475 | 743 | 0 | 488 | 0 |
N.S. |
1 | 1.05 | 0.96 | 1.43 | 1.60 | 1.29 | 2.02 | 0.00 | 1.33 | 0.00 |
time (sec) |
N/A | 1.056 | 0.329 | 2.860 | 0.069 | 0.099 | 0.502 | 0.000 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 239 | 262 | 248 | 364 | 378 | 319 | 454 | 0 | 344 | 0 |
N.S. |
1 | 1.10 | 1.04 | 1.52 | 1.58 | 1.33 | 1.90 | 0.00 | 1.44 | 0.00 |
time (sec) |
N/A | 0.799 | 0.222 | 2.239 | 0.059 | 0.113 | 0.352 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 162 | 142 | 183 | 219 | 183 | 233 | 0 | 232 | 0 |
N.S. |
1 | 1.16 | 1.01 | 1.31 | 1.56 | 1.31 | 1.66 | 0.00 | 1.66 | 0.00 |
time (sec) |
N/A | 0.629 | 1.004 | 1.408 | 0.043 | 0.096 | 0.254 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 50 | 74 | 72 | 72 | 96 | 82 | 111 | 73 | 0 |
N.S. |
1 | 1.09 | 1.61 | 1.57 | 1.57 | 2.09 | 1.78 | 2.41 | 1.59 | 0.00 |
time (sec) |
N/A | 0.400 | 0.033 | 0.508 | 0.046 | 0.095 | 0.117 | 0.198 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 291 | 285 | 273 | 0 | 0 | 0 | 0 | 0 | 55 | 0 |
N.S. |
1 | 0.98 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 1.714 | 0.176 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 263 | 239 | 191 | 525 | 0 | 0 | 0 | 0 | 149 | 0 |
N.S. |
1 | 0.91 | 0.73 | 2.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 1.290 | 0.136 | 5.752 | 0.000 | 0.000 | 0.000 | 0.000 | 10.286 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 349 | 331 | 270 | 815 | 0 | 0 | 0 | 0 | 308 | 0 |
N.S. |
1 | 0.95 | 0.77 | 2.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 1.443 | 0.399 | 6.426 | 0.000 | 0.000 | 0.000 | 0.000 | 0.340 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 394 | 378 | 305 | 394 | 0 | 0 | 0 | 0 | 79 | 0 |
N.S. |
1 | 0.96 | 0.77 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 1.412 | 0.460 | 4.467 | 0.000 | 0.000 | 0.000 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 245 | 233 | 188 | 254 | 0 | 0 | 0 | 0 | 55 | 0 |
N.S. |
1 | 0.95 | 0.77 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.934 | 0.301 | 3.828 | 0.000 | 0.000 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 110 | 98 | 120 | 0 | 0 | 0 | 0 | 31 | 0 |
N.S. |
1 | 0.95 | 0.84 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.811 | 0.133 | 3.147 | 0.000 | 0.000 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 49 | 45 | 56 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 0.91 | 0.83 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.684 | 0.041 | 0.971 | 0.000 | 0.000 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 20 | 25 | 15 | 20 | 27 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.39 | 0.83 | 1.11 | 1.50 | 1.11 |
time (sec) |
N/A | 0.344 | 0.155 | 1.362 | 0.097 | 0.090 | 0.944 | 0.132 | 0.204 | 2.624 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 20 | 49 | 17 | 20 | 55 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 2.72 | 0.94 | 1.11 | 3.06 | 1.11 |
time (sec) |
N/A | 0.343 | 0.272 | 0.908 | 0.107 | 0.095 | 1.897 | 0.770 | 0.207 | 2.663 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 359 | 359 | 288 | 616 | 0 | 0 | 0 | 0 | 97 | 0 |
N.S. |
1 | 1.00 | 0.80 | 1.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 1.188 | 1.499 | 3.988 | 0.000 | 0.000 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 180 | 150 | 272 | 0 | 0 | 0 | 0 | 59 | 0 |
N.S. |
1 | 1.00 | 0.83 | 1.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.568 | 0.800 | 3.318 | 0.000 | 0.000 | 0.000 | 0.000 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 89 | 71 | 118 | 0 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.05 | 0.84 | 1.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.653 | 0.139 | 1.118 | 0.000 | 0.000 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 746 | 51 | 17 | 20 | 58 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 41.44 | 2.83 | 0.94 | 1.11 | 3.22 | 1.11 |
time (sec) |
N/A | 0.234 | 5.589 | 0.863 | 0.642 | 0.087 | 1.788 | 0.144 | 0.196 | 2.639 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 1050 | 92 | 19 | 20 | 109 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 58.33 | 5.11 | 1.06 | 1.11 | 6.06 | 1.11 |
time (sec) |
N/A | 0.227 | 4.021 | 0.919 | 1.084 | 0.094 | 7.032 | 1.215 | 0.225 | 2.764 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 271 | 32 | 17 | 20 | 117 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 15.06 | 1.78 | 0.94 | 1.11 | 6.50 | 1.11 |
time (sec) |
N/A | 0.577 | 4.654 | 1.961 | 0.782 | 0.099 | 6.686 | 0.214 | 0.206 | 2.866 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 179 | 0 | 0 | 0 | 0 | 0 | 0 | 66 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.351 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 20 | 20 | 15 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.11 | 0.83 | 1.11 | 1.11 | 1.11 |
time (sec) |
N/A | 0.239 | 0.268 | 2.231 | 0.088 | 0.085 | 0.986 | 0.130 | 200.026 | 2.627 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 607 | 34 | 17 | 20 | 34 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 33.72 | 1.89 | 0.94 | 1.11 | 1.89 | 1.11 |
time (sec) |
N/A | 0.229 | 0.578 | 2.095 | 0.775 | 0.092 | 10.613 | 0.133 | 0.217 | 2.655 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 620 | 363 | 410 | 1309 | 0 | 0 | 0 | 0 | 335 | 0 |
N.S. |
1 | 0.59 | 0.66 | 2.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 1.191 | 0.724 | 1.317 | 0.000 | 0.000 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 425 | 257 | 301 | 913 | 0 | 0 | 0 | 0 | 231 | 0 |
N.S. |
1 | 0.60 | 0.71 | 2.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 1.351 | 0.684 | 1.294 | 0.000 | 0.000 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 136 | 208 | 582 | 0 | 0 | 0 | 0 | 129 | 0 |
N.S. |
1 | 0.62 | 0.94 | 2.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.691 | 0.847 | 1.622 | 0.000 | 0.000 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 664 | 461 | 1358 | 747 | 0 | 0 | 0 | 0 | 124 | 0 |
N.S. |
1 | 0.69 | 2.05 | 1.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 2.573 | 4.502 | 1.544 | 0.000 | 0.000 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 781 | 572 | 1384 | 1701 | 0 | 0 | 0 | 0 | 461 | 0 |
N.S. |
1 | 0.73 | 1.77 | 2.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 2.777 | 7.441 | 1.602 | 0.000 | 0.000 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 868 | 488 | 536 | 2079 | 0 | 0 | 0 | 0 | 544 | 0 |
N.S. |
1 | 0.56 | 0.62 | 2.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 2.010 | 1.504 | 1.432 | 0.000 | 0.000 | 0.000 | 0.000 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 619 | 359 | 416 | 1568 | 0 | 0 | 0 | 0 | 383 | 0 |
N.S. |
1 | 0.58 | 0.67 | 2.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 1.527 | 1.082 | 1.368 | 0.000 | 0.000 | 0.000 | 0.000 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 331 | 188 | 289 | 1065 | 0 | 0 | 0 | 0 | 224 | 0 |
N.S. |
1 | 0.57 | 0.87 | 3.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.659 | 0.600 | 1.868 | 0.000 | 0.000 | 0.000 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 974 | 641 | 2869 | 1557 | 0 | 0 | 0 | 0 | 320 | 0 |
N.S. |
1 | 0.66 | 2.95 | 1.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 2.293 | 11.884 | 1.454 | 0.000 | 0.000 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1142 | 617 | 810 | 2884 | 0 | 0 | 0 | 0 | 754 | 0 |
N.S. |
1 | 0.54 | 0.71 | 2.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 1.471 | 2.010 | 1.560 | 0.000 | 0.000 | 0.000 | 0.000 | 0.255 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 837 | 470 | 555 | 2309 | 0 | 0 | 0 | 0 | 536 | 0 |
N.S. |
1 | 0.56 | 0.66 | 2.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.64 | 0.00 |
time (sec) |
N/A | 1.557 | 1.571 | 1.454 | 0.000 | 0.000 | 0.000 | 0.000 | 0.230 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 455 | 249 | 390 | 1679 | 0 | 0 | 0 | 0 | 320 | 0 |
N.S. |
1 | 0.55 | 0.86 | 3.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.70 | 0.00 |
time (sec) |
N/A | 1.125 | 0.801 | 2.009 | 0.000 | 0.000 | 0.000 | 0.000 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1500 | 945 | 7168 | 3499 | 0 | 0 | 0 | 0 | 564 | 0 |
N.S. |
1 | 0.63 | 4.78 | 2.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 2.881 | 22.883 | 1.642 | 0.000 | 0.000 | 0.000 | 0.000 | 5.622 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 406 | 256 | 304 | 785 | 0 | 0 | 0 | 0 | 249 | 0 |
N.S. |
1 | 0.63 | 0.75 | 1.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.863 | 1.097 | 1.469 | 0.000 | 0.000 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 246 | 158 | 233 | 484 | 0 | 0 | 0 | 0 | 162 | 0 |
N.S. |
1 | 0.64 | 0.95 | 1.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.698 | 0.702 | 1.426 | 0.000 | 0.000 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | F | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 84 | 158 | 227 | 87 | 0 | 0 | 0 | 79 | 0 |
N.S. |
1 | 0.74 | 1.39 | 1.99 | 0.76 | 0.00 | 0.00 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 0.552 | 0.352 | 1.849 | 0.041 | 0.000 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 76 | 77 | 28 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.00 | 1.62 | 1.64 | 0.60 | 0.00 | 0.00 | 0.00 | 0.79 | 0.00 |
time (sec) |
N/A | 0.333 | 0.036 | 0.520 | 0.036 | 0.000 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 325 | 238 | 240 | 529 | 0 | 0 | 0 | 0 | 157 | 0 |
N.S. |
1 | 0.73 | 0.74 | 1.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 1.632 | 0.340 | 1.368 | 0.000 | 0.000 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 438 | 327 | 251 | 1770 | 0 | 0 | 0 | 0 | 607 | 0 |
N.S. |
1 | 0.75 | 0.57 | 4.04 | 0.00 | 0.00 | 0.00 | 0.00 | 1.39 | 0.00 |
time (sec) |
N/A | 1.657 | 0.418 | 1.538 | 0.000 | 0.000 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 36 | 32 | 34 | 34 | 0 | 34 | 35 | 34 |
N.S. |
1 | 1.00 | 1.06 | 0.94 | 1.00 | 1.00 | 0.00 | 1.00 | 1.03 | 1.00 |
time (sec) |
N/A | 0.391 | 0.107 | 8.298 | 0.737 | 0.126 | 0.000 | 48.234 | 0.232 | 2.781 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 438 | 426 | 397 | 0 | 0 | 0 | 0 | 0 | 98 | 0 |
N.S. |
1 | 0.97 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 1.763 | 0.143 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 332 | 328 | 304 | 0 | 0 | 0 | 0 | 0 | 59 | 0 |
N.S. |
1 | 0.99 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 1.307 | 0.150 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 197 | 196 | 206 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.99 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 1.156 | 0.016 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 36 | 32 | 34 | 51 | 31 | 34 | 44 | 34 |
N.S. |
1 | 1.00 | 1.06 | 0.94 | 1.00 | 1.50 | 0.91 | 1.00 | 1.29 | 1.00 |
time (sec) |
N/A | 0.550 | 0.286 | 5.250 | 0.704 | 0.082 | 8.790 | 0.461 | 0.212 | 2.699 |